1. Field of the Invention
The invention relates to digital frequency synthesizers, and in particular to the reduction of noise in such synthesizers.
2. Description of the Prior Art
Direct Digital Frequency Synthesis (DDFS or DDS) is a technique for generating digital frequency signals. FIG. 1 is a schematic block diagram of a frequency synthesizer for implementing the technique.
In FIG. 1 a phase accumulator 12 repeatedly accumulates a phase value 14 (a phase increment is often called a constant frequency word (FW) or delta-phase word) to generate samples 16 of a digital sawtooth signal, and a look-up table 18 of digital samples for converting the digital sawtooth signal to a digital waveshape for the digital frequency signal 20. The digital samples stored in the look-up table 18 are typically either sine or cosine values for generating a sine wave as the digital frequency signal. A clock 22, which can be external or internal, provides a clock signal CK at a frequency C which allows the digital frequency synthesizer to generate any frequency between 0 and approximately 0.4C.
The generated frequency f is related to the constant frequency word (FW) and the accumulator length L by: f=C * FW/2.sup.L.
The frequency resolution is C/2.sup.L.For example, with a reference clock at 100 MHZ and a 32-bit accumulator, the resolution is 0.023Hz.
FIGS. 2A-2D illustrate the steps in this process as performed by the apparatus of FIG. 1. As illustrated in FIG. 2A, by adding a constant frequency word 14 on every clock signal CK of the clock 22 to an accumulator 12, and arranging for this to operate in a cyclic fashion, it is possible to generate a sawtooth waveform SW. The sawtooth waveform is sampled by reading out the accumulated values at 16once per clock signal CK. For a given clock frequency and accumulator resolution, the larger the value of the constant frequency word, the higher the frequency of the sawtooth waveform.
As illustrated in FIG. 2B, the sawtooth waveform samples are used to address the digital waveform samples in the look-up table 18. Typically, the address resolution of the look-up table 18 is less than the resolution of the accumulator 12. Accordingly, the sawtooth waveform samples are truncated in order to generate the look-up table addresses 17.
The digital frequency signal 20 is output as a series of digital waveform samples, with a digital waveshape sample being generated for each clock signal CK. FIG. 2C is a schematic representation of a smooth waveform (typically, in practice, a sine wave) and FIG. 2D is a schematic representation of the resulting digital waveshape of the digital frequency signal, which is quantized and therefore does not exactly correspond to the smooth waveform.
Synthesizers of this type are particularly effective as a technique for generating frequency signals where rapid frequency switching is required because the frequency switching time is much less than comparable analog frequency synthesizers that may be used as modulators.
Accordingly, this technique is widely used in the design of digital modulators, for example quadrature amplitude modulators and phase switched keying modulators (M-QAM, M-PSK), and for frequency hopping modems and the like.
However, conventional digital frequency synthesizers suffer from noise problems due to the presence of spurious spectral lines in the frequency signals they generate.
It has been determined that the spectral lines arise from a number of sources as follows:
1) Although the interval between the phase accumulator overflows is not strictly constant, the overflow is a periodic signal, with a period equal to the lowest common multiplier of the constant frequency word and 2.sup.N.
2) The sawtooth signal is truncated before addressing the look-up table, which creates quantization noise, which is also periodic, with a period equal to the sawtooth signal, that is equal to the lowest common multiplier of the constant frequency word and 2.sup.N.
3) The look-up table contains quantized digital samples of the waveshape (typically sine or cosine) values which adds to the quantization error.
4) If a Digital to Analog Converter (DAC) is used to convert the sine samples to an analog signal, its non-linearity also introduces a periodic noise source.
All of these signals generate discrete spurious spectral lines which can be as high as -40 dBc from the main signal as represented in FIG. 3. Conventionally, to reduce the effects of the spurious spectral lines, a very large look-up table is used. In particular many address bits are used to minimize the effects of phase truncation (the second noise source in the above list) and a large look-up table word size is used to minimize the sample quantization noise (the third word noise source in the above list).